Identifier
Identifier
Values
[1,0] generating graphics... => 2
[1,0,1,0] generating graphics... => 3
[1,1,0,0] generating graphics... => 3
[1,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,0,1,0] generating graphics... => 7
[1,0,1,0,1,1,0,0] generating graphics... => 6
[1,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,0] generating graphics... => 6
[1,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 9
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 8
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 7
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 7
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 7
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 7
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 7
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 8
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 6
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 5
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 6
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 8
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 7
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 6
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 7
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 8
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 9
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 7
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 6
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 7
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 6
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 7
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 6
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 6
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 11
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 10
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 9
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 9
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 9
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 9
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 8
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 9
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 10
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 8
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 8
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 7
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 7
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 8
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 9
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 8
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 7
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 7
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 7
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 9
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 8
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 10
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 11
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 9
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 7
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 7
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 8
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 7
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 8
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 7
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 7
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 8
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 7
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 8
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 8
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 6
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 7
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 6
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 5
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 7
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 10
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 9
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 8
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 8
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 8
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 8
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 7
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 8
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 9
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 7
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 7
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 6
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 7
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 9
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 8
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 7
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 7
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 7
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 10
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 9
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 11
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 12
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 10
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 8
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 8
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 9
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 8
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 7
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 7
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 8
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 6
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 8
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 9
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 9
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 7
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 6
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 6
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 9
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 8
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 7
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 7
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 7
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 8
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 7
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 9
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 10
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 8
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 6
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 7
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 6
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 7
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 6
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 8
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 9
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 7
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 8
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 9
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 10
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 7
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 6
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 8
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 7
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 7
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 8
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 6
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 7
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 7
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 5
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 6
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 6
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 4
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 7
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 7
click to show generating function       
Description
Number of indecomposable reflexive modules in the corresponding Nakayama algebra.
Code
DeclareOperation("IsNthSyzygy",[IsList]);

InstallMethod(IsNthSyzygy, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h,W;

M:=LIST[1];

n:=LIST[2];

N:=DualOfModule(NthSyzygy(DualOfModule(M),n));

W:=NthSyzygy(N,n);

if IsDirectSummand(M,W)=true
then
return(1);
else return(0);
fi;
end);


DeclareOperation("NumberOfReflexiveModules",[IsList]);

InstallMethod(NumberOfReflexiveModules, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h,W;

L:=LIST[1];

A:=NakayamaAlgebra(L,GF(3));
L:=ARQuiver([A,1000])[2];
LL1:=Filtered(L,x->DominantDimensionOfModule(x,30)>=1);
LL2:=Filtered(LL1,x->IsNthSyzygy([x,2])=1);
return(Size(LL2));


end);
Created
Dec 30, 2017 at 17:27 by Rene Marczinzik
Updated
Dec 30, 2017 at 17:27 by Rene Marczinzik